feat(connect): let hosts set their display name

[PixPMusic]

Summary

• add a host-local Host name setting under Settings → Connections for web and desktop
• use the configured name in live environment descriptors and as the default for newly paired manual connections
• refresh relay-managed environment labels from verified health responses so renamed hosts propagate to other clients
• fall back to the existing OS-detected computer name when the setting is cleared
• keep web and mobile environment presentation in sync with the live server descriptor

Why

T3 Connect environment names were derived from the host operating system with no supported override. Relay-managed machines, especially remote hosts, could not choose a useful display name from the host itself.

Before / After

Before

After

The screenshots use an isolated test environment and the neutral example “Studio Mac”; no real machine hostname is shown.

Verification

• vp test run packages/contracts/src/settings.test.ts apps/server/src/environment/ServerEnvironment.test.ts packages/client-runtime/src/state/server.test.ts packages/client-runtime/src/relay/discovery.test.ts infra/relay/src/environments/EnvironmentConnector.test.ts infra/relay/src/environments/EnvironmentLinks.test.ts infra/relay/src/agentActivity/AgentActivityPublisher.test.ts infra/relay/src/agentActivity/MobileRegistrations.test.ts infra/relay/src/environments/EnvironmentLinker.test.ts infra/relay/src/http/Api.test.ts — 105 tests passed
• vp run --filter @t3tools/contracts --filter @t3tools/client-runtime --filter t3 --filter @t3tools/web --filter @t3tools/mobile --filter t3code-relay --concurrency-limit 2 typecheck
• targeted formatting and lint for all changed files
• git diff --check
• isolated test-t3-app pass: verified the new row is absent on main, setting “Studio Mac” persists, and Connections renders the configured name without exposing the system hostname

Checklist

• This PR is small and focused
• I explained what changed and why
• I added regression coverage
• I included before/after UI evidence

Note

Let hosts set a custom display name for their environment

• Adds environmentLabel to ServerSettings and ServerSettingsPatch schemas, defaulting to empty string when unset.
• ServerEnvironment.getDescriptor now returns the persisted environmentLabel from settings when non-empty, falling back to the default label on read failure with a warning.
• The Connections Settings page gains a "Host name" input field that writes to environmentLabel via updatePrimarySettings.
• settingsUpdated WebSocket events now include the current environment descriptor, and the client-side projection in applyServerConfigProjection applies it.
• The relay's EnvironmentConnector persists label changes reported in health responses via the new EnvironmentLinks.updateLabelForUser API, and relay discovery updates the stored label from status responses.

^{Macroscope summarized f7d7c28.}

Model: GPT-5.6 Sol | Harness: Codex in T3 Code

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Cursor Bugbot has reviewed your changes using high effort and found 1 potential issue.

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[macroscopeapp]

Approvability

Verdict: Needs human review

This PR introduces a new user-facing feature allowing hosts to set custom display names, with changes spanning contracts, server settings, relay infrastructure (database updates), WebSocket payloads, and UI components. New features with this scope warrant human review.

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